Question

1. each lap around a track is 400 meters. jane is training for a marathon and runs four laps on the track in 7.75 minutes.

a. what is her total displacement?
b. what is her average velocity?
c. what is her average speed in meters per minute?

Explanation:

Part a

Step1: Understand Displacement

Displacement is the straight - line distance from the initial position to the final position. When Jane runs four laps around a circular track, she starts and ends at the same point.
So, her initial position and final position are the same.

Step2: Calculate Displacement

If the initial position \(x_i\) is equal to the final position \(x_f\), then displacement \(d=x_f - x_i\). Since she ends up where she started, \(x_f=x_i\), so \(d = 0\) meters.

Step1: Recall Average Velocity Formula

Average velocity \(v_{avg}=\frac{\text{displacement}}{\text{time}}\)

Step2: Substitute Values

We know from part (a) that displacement \(d = 0\) meters and time \(t=7.75\) minutes.
So, \(v_{avg}=\frac{0}{7.75}=0\) meters per minute.

Step1: Calculate Total Distance

Each lap is 400 meters and she runs 4 laps. So total distance \(s=400\times4 = 1600\) meters.

Step2: Recall Average Speed Formula

Average speed \(v=\frac{\text{total distance}}{\text{time}}\)

Step3: Substitute Values

Total distance \(s = 1600\) meters and time \(t = 7.75\) minutes.
So, \(v=\frac{1600}{7.75}\approx206.45\) meters per minute (rounded to two decimal places).

Answer:

0 meters

Part b